meshfree_interpolation.h

// The libMesh Finite Element Library.
// Copyright (C) 2002-2012 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



#ifndef LIBMESH_MESHFREE_INTERPOLATION_H
#define LIBMESH_MESHFREE_INTERPOLATION_H

// Local includes
#include "libmesh/libmesh_config.h"
#include "libmesh/libmesh_common.h"
#include "libmesh/auto_ptr.h"
#include "libmesh/point.h"
#ifdef LIBMESH_HAVE_NANOFLANN
#  include "libmesh/nanoflann.hpp"
#endif

// C++ includes
#include <string>
#include <vector>



namespace libMesh
{

/**
 * Base class to support various mesh-free interpolation methods.
 * Such methods can be useful for example to pass data between 
 * two different domains which share a physical boundary, where
 * that boundary may be discretized differently in each domain.
 * This is the case for conjugate heat transfer applications where
 * the common interface has overlapping but distinct boundary 
 * discretizations.
 */
class MeshfreeInterpolation
{
public:

  /**
   * Constructor.
   */
  MeshfreeInterpolation () 
  {}

  /**
   * Prints information about this object, by default to
   * libMesh::out.
   */
  void print_info (std::ostream& os=libMesh::out) const;

  /**
   * Same as above, but allows you to also use stream syntax.
   */
  friend std::ostream& operator << (std::ostream& os, const MeshfreeInterpolation& mfi);

  /**
   * Clears all internal data structures and restores to a
   * pristine state.
   */
  virtual void clear();

  /**
   * The number of field variables.
   */
  unsigned int n_field_variables () const 
  { return _names.size(); }
  
  /**
   * Defines the field variable(s) we are responsible for,
   * and importantly their assumed ordering.
   */
  void set_field_variables (const std::vector<std::string> &names)
  { _names = names; }

  /**
   *@returns the field variables as a read-only reference.
   */
  const std::vector<std::string> & field_variables() const
  { return _names; }
  
  /**
   * @returns a writeable reference to the point list.
   */
  std::vector<Point> & get_source_points ()
  { return _src_pts; }
  
  /**
   * @returns a writeable reference to the point list.
   */
  std::vector<Real> & get_source_vals ()
  { return _src_vals; }

  /**
   * Sets source data at specified points.
   */     
  virtual void add_field_data (const std::vector<std::string> &field_names,
			       const std::vector<Point>  &pts,
			       const std::vector<Number> &vals);

  /**
   * Interpolate source data at target points.
   * Pure virtual, must be overriden in derived classes.
   */
  virtual void interpolate_field_data (const std::vector<std::string> &field_names,
				       const std::vector<Point>  &tgt_pts,
				       std::vector<Number> &tgt_vals) const = 0;

protected:
    
  std::vector<std::string> _names;
  std::vector<Point>       _src_pts;
  std::vector<Number>      _src_vals;
};



/**
 * Inverse distance interplation.
 */
template <unsigned int KDDim>
class InverseDistanceInterpolation : public MeshfreeInterpolation
{
private:

#ifdef LIBMESH_HAVE_NANOFLANN  
  /**
   * This class adapts list of libMesh \p Point types
   * for use in a nanoflann KD-Tree. For more on the 
   * basic idea see examples/pointcloud_adaptor_example.cpp
   * in the nanoflann source tree.
   */
  template <unsigned int PLDim>
  class PointListAdaptor
  {    
  private:
    const std::vector<Point> &_pts;

  public:
    PointListAdaptor (const std::vector<Point> &pts) :
      _pts(pts)
    {}

    /**
     * libMesh \p Point coordinate type
     */
    typedef Real coord_t;

    /**
     * Must return the number of data points
     */
    inline size_t kdtree_get_point_count() const { return _pts.size(); }
    
    /**
     * Returns the distance between the vector "p1[0:size-1]" 
     * and the data point with index "idx_p2" stored in the class
     */
    inline coord_t kdtree_distance(const coord_t *p1, const size_t idx_p2, size_t size) const
    {
      libmesh_assert_equal_to (size, PLDim);
      libmesh_assert_less (idx_p2, _pts.size());

      const Point &p2(_pts[idx_p2]);

      switch (size)
	{
	case 3:
	  {
	    const coord_t d0=p1[0] - p2(0);
	    const coord_t d1=p1[1] - p2(1);
	    const coord_t d2=p1[2] - p2(2);

	    return d0*d0 + d1*d1 + d2*d2;
	  }
	 
	case 2:
	  {
	    const coord_t d0=p1[0] - p2(0);
	    const coord_t d1=p1[1] - p2(1);

	    return d0*d0 + d1*d1;
	  }
	 
	case 1:
	  {
	    const coord_t d0=p1[0] - p2(0);

	    return d0*d0;
	  }
	 
	default:
	  libMesh::err << "ERROR: unknown size " << size << std::endl;
	  libmesh_error();
	}

      return -1.;
    }
    
    /**
     * Returns the dim'th component of the idx'th point in the class:
     * Since this is inlined and the "dim" argument is typically an immediate value, the
     *  "if's" are actually solved at compile time.
     */
    inline coord_t kdtree_get_pt(const size_t idx, int dim) const
    {
      libmesh_assert_less (dim, (int) PLDim);
      libmesh_assert_less (idx, _pts.size());
      libmesh_assert_less (dim, 3);

      const Point &p(_pts[idx]);

      if (dim==0) return p(0);
      if (dim==1) return p(1);
      return p(2);
    }
    
    /**
     * Optional bounding-box computation: return false to default to a standard bbox computation loop.
     * Return true if the BBOX was already computed by the class and returned in "bb" so it can be 
     * avoided to redo it again. Look at bb.size() to find out the expected dimensionality 
     * (e.g. 2 or 3 for point clouds)
     */
    template <class BBOX>
    bool kdtree_get_bbox(BBOX & /* bb */) const { return false; }
  };

  PointListAdaptor<KDDim> _point_list_adaptor;

  // template <int KDDIM>
  // class KDTree : public KDTreeSingleIndexAdaptor<L2_Simple_Adaptor<num_t, PointListAdaptor >,
  // 						 PointListAdaptor,
  // 						 KDDIM>
  // {
  // };

  typedef nanoflann::KDTreeSingleIndexAdaptor<nanoflann::L2_Simple_Adaptor<Real, PointListAdaptor<KDDim> >,
					      PointListAdaptor<KDDim>, KDDim> kd_tree_t;

  mutable AutoPtr<kd_tree_t> _kd_tree;

#endif // LIBMESH_HAVE_NANOFLANN

  /**
   * Build & initialize the KD tree, if needed.
   */
  void construct_kd_tree ();

  /**
   * Performs inverse distance interpolation at the input point from
   * the specified points.
   */
  void interpolate (const Point               &pt,
		    const std::vector<size_t> &src_indices,
		    const std::vector<Real>   &src_dist_sqr,
		    std::vector<Number>::iterator &out_it) const;
  
  const unsigned int _half_power;
  const unsigned int _n_interp_pts;

  /**
   * Temporary work array.  Object level scope to avoid cache thrashing.
   */  
  mutable std::vector<Number> _vals;
  
public:

  /**
   * Constructor. Takes the inverse distance power, 
   * which defaults to 2. 
   */
  InverseDistanceInterpolation (const unsigned int n_interp_pts = 8,
				const unsigned int power        = 2) :
    MeshfreeInterpolation(),
#if LIBMESH_HAVE_NANOFLANN
    _point_list_adaptor(_src_pts),
#endif
    _half_power(power/2),
    _n_interp_pts(n_interp_pts)
  {
    libmesh_assert_greater_equal (power, 2);
  }
  
  /**
   * Interpolate source data at target points.
   * Pure virtual, must be overriden in derived classes.
   */
  virtual void interpolate_field_data (const std::vector<std::string> &field_names,
				       const std::vector<Point>  &tgt_pts,
				       std::vector<Number> &tgt_vals) const;

};

} // namespace libMesh


#endif // #define LIBMESH_MESHFREE_INTERPOLATION_H